Preheat oven to 350 degrees F. Line two large baking sheets with parchment paper.
Combine melted butter, egg and sugars in a large bowl or bowl of your stand mixer fitted with the paddle attachment. Mix vigorously for about 1 minute. Add pumpkin pie filling, molasses, cinnamon, nutmeg, ginger, allspice, baking soda and salt. Mix for another minute to combine.
Using a sturdy spatula or wooden spoon, fold flour into wet mixture. Using a small ice cream scoop, drop dough onto prepared baking sheets. Bake for 10 minutes, or until tops of cookies spring back lightly when touched.
Once cookies are completely cooled, combine softened cream cheese and powdered sugar in a large bowl. Beat well to combine until smooth. If desired, add a little milk or cream to thin frosting. Frost cookies.
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